A stochastic approach to analyze trade-offs and risks associated with large-scale water resources systems

Water resources development projects often involve multiple and conflicting objectives as well as stochastic hydrologic inputs. Multiobjective optimization techniques can be used to identify noninferior solutions and to construct a trade-off relationship between conflicting objectives. This paper presents a methodology for analyzing trade-offs and risks associated with large-scale water resource projects under hydrologic uncertainty. The proposed methodology relies on the stochastic dual dynamic programming (SDDP) model to derive monthly or weekly operating rules for multipurpose multireservoir systems taking into account the stochasticity of the inflows, irrigation water withdrawals, minimum/maximum flow requirements for navigation, fishing, and/or for ecological purposes. In SDDP, release decisions are chosen so as to minimize the operating costs of a hydrothermal electrical system. Irrigation water demands and other operating constraints are imposed on the system through the SDDP model. The proposed methology is illustrated with the Southeastern Anatolia Development project, commonly called GAP, in Turkey. The GAP is a multidimensional development project involving primarily the production of hydroelectricity and irrigation. Simulation results using 50 hydrologic scenarios show that the complete development of the irrigation projects would reduce the total energy output by 6.5% and will increase the risk of not meeting minimum outflow at the Syrian border from 5% to 25%.

Creating Harmony in South America: The Challenge of Conciliating Energy Development & Environmental Constraints in South America

South America is looking for ways to harmonize power supply expansion with growing environmental concerns as electricity demand increases at a fast pace. While South America contributed little to the world’s total pollutant emissions,societies are increasingly becoming aware of the impact that new hydropower plants or fossil-burning thermal generators have. And the “not in my backyard” syndrome, typical of developed countries, is also gaining strength in the region. Private investors leading key investment decisions in the reformed South American power sectors are facing organized opposition to the building of new plants. Brazil and Chile provide two examples of how countries are trying to reconcile the need for abundant energy supply with environmental constraints

Nash Equilibrium in Strategic Bidding: A Binary Expansion Approach

This paper presents a mixed integer linear programming solution approach for the equilibrium problem with equilibrium constraints (EPEC) problem of finding the Nashequilibrium (NE) in strategic bidding in short-term electricity markets. A binary expansion (BE) scheme is used to transform the nonlinear, nonconvex, NE problem into a mixed integer linear problem (MILP), which can be solved by commercially available computational systems. The BE scheme can be applicable to Cournot, Bertrand, or joint price/quantity bidding models. The approach is illustrated in case studies with configurations derived from the 95-GW Brazilian system, including unit-commitment decisions to the price-maker agents.

Allocation of Firm-Energy Rights among Hydro agents using Cooperative Game Theory: an Aumann-Shapley approach

The objective of this work is to investigate the application of different methodologies of allocation of firm energy rights among hydro plants using a cooperative game-theoretic framework. It is shown that there is not an optimal and unique approach to make this allocation, but there are criteria to verify if a given approach presents any drawbacks. One of these criteria is the “justice”, or “fairness”. It is shown that this criterion is equivalent to the condition of the core of a cooperative game. The calculation of the total firm energy will be based on the solution of a linear programming problem. The paper investigates the advantages and disadvantages of different methods to allocate the firm energy, such as marginal allocation, average production on the critical period, incremental allocation rights, “nucleolus” and Auman-Shapley (AS). It is shown that, besides being robust and computationally efficient, the AS allocation lies in the core of the game and, thus, meets the condition of “justice”. Some methods will be applied to the Brazilian system (composed of about 100 hydro plants) and the results will be compared with the allocation method currently adopted in the regulations of the country.

The integration of natural gas and electricity sectors has increased sharply in the last decade as a consequence of combined cycle natural gas thermal power plants. In some countries such as Brazil, gas-fired generation has been a major factor in the overall growth of natural gas consumption. Brazil’s National System Operator dispatches these gas-fired plants (along with other thermal sources such as coal, oil and nuclear) in conjunction with the country’s hydroelectric plants using a stochastic dual dynamic programming (SDDP) scheme. The SDDP algorithm determines the optimal hydro-to-thermal energy production ratio based on the expected benefit of reducing thermal plant generation over a large number of hydrological scenarios, along a planning horizon of five years. This means that the optimal scheduling decision today depends on assumptions about future load growth and future entrance of new generation capacity. However, the hydrothermal scheduling model does not take into account the possibility of future fuel supply constraints, either in production or in transportation. The assumption of fuel supply adequacy is felt to be reasonable for the more mature markets such as coal and oil. However, due to the fast growth of the natural gas market, it is possible that demand outpaces supply and/or transportation investments. A first indication that gas-related constraints could be relevant took place in January 2004, when 800 MW of combined-cycle generation (out of a total capacity of 1200 MW) could not be dispatched due to constraints in pipeline capacity. The objective of this work is present a methodology for representing the natural gas supply, demand and transportation network in the stochastic hydrothermal power scheduling model. Gas demand in each node is given by the sum of non-power gas consumption forecasts plus gas consumption factors for the gas-fired power plants; gas production in each node is represented as minimum and maximum production levels, depending for example if the gas field is associated with oil production. Finally, fuel transportation is modeled both through pipelines and through LNG. The application of the integrated electricity-gas scheduling model is illustrated in case studies with realistic configurations of the 90 GW Brazilian system.

Auctions of Contracts and Energy Call Options to Ensure Supply Adequacy in the Second Stage of the Brazilian Power Sector Reform

The reform process in the electricity sector of any country has as main objective the design of a power market capable to induce a reliable and efficient energy supply, translated into adequate tariffs. Brazil started its reform process in 1996, inspired by similar schemes in the electricity sector of more developed countries. However, the existence of particularities in the country’s hydroelectric energy market, such as weak spot price signals for system expansion and difficulties to determine benchmark prices, avoided a smooth transition to a fully deregulated market. In 2004, a revisited power sector model was launched, aiming at alleviating the difficulties of the first model. The core of the new proposals lies on the use of contract obligation and energy supply auctions as the backbone for the efficient contracting and supply adequacy. Supply auctions were held in 2004-2005, with a volume of about 20,000 average MW contracted involving about 60 billion USD in financial transactions. This work discusses the implementation of auctions of energy contracts and call options in Brazil as part of the mechanisms to ensure supply adequacy adopted in the second stage of its power sector reform.

The optimal scheduling of hydrothermal systems requires the representation of future inflows uncertainties for basically two reasons. Firstly, to define the present day commitment of thermal plants in order to hedge against adverse low inflows, and, secondly, to specify the volume of water storage in reservoirs to avoid spillage if high inflows occur. An inflow scenario tree must be correctly dimensioned so as to provide a parsimonious — but still representative — sample of the multivariate process underlying possible future inflows. In this article we propose a methodology to generate such a tree. The idea is to use principal component analysis to reduce the effective dimensionality of the scenario specification problem so that a discretization technique can be used in a smaller dimensional space. A stochastic hydrothermal scheduling optimization model was applied to the Brazilian interconnected power system to illustrate the proposed methodology. The quality of the reduced sample was evaluated by considering not only hydrological aspects, but also the solution stability of the stochastic problem.

The objective of this article is to present a benchmarking of financial indicators implemented in hydroelectric stochastic risk management models. We present three model formulations using a tree approach for hydroelectric optimisation using three procedures for financial risk control: Minimum Revenues (Rmin), Value-at-Risk (VaR) and Conditional VaR (CVaR). According to their properties and their formulation in each model we compare them theoretically based on two criteria: their adequacy for electricity portfolio optimisation subject to risk constraints and the feasibility of their implementation inside the state of the art (SDDP) algorithm appropriate for large scale energy systems. Using numerical examples we verify the statements derived from the theoretical comparison.

The objective of this paper is to present the operating and hedging analysis of a hydroelectric system in a non-hydro dominated market using a specifically-developed tool for operating and contracting decisions. Hydropower companies are likely to face stochastic inflows, spot prices, and forward prices, during their operation. The objective of the tool is to maximize expected revenues from spot and forward market trading, considering suitable indicators of the company risk aversion. We benchmark the implemented risk indicator of required Minimum Revenues in the optimization tool using financial risk indicators, such as Value at Risk, Conditional Value at Risk, and the Risk Premium of a Utility function. This portfolio management problem, which includes physical and financial assets, is formulated as a stochastic revenue maximization problem under a specified risk aversion constraint. The company risk aversion is apprehended by penalizing reservoir operation and derivative instruments contracting decisions policies that lead to financial performances that are violating the required Minimum Revenues at the end of a predefined profit period. A hybrid Stochastic Dynamic Programming (SDP) / Stochastic Dual Dynamic Programming (SDDP) formulation is adopted to solve this large-scale optimization problem.

The network loading of a hydrothermal system is highly variable due to several factors. Hydro plants are usually located in different river basins, usually far from load centers. Diversity of streamflows along these basins lead to distinct generation dispatches, sometimes inverting energy interchanges between hydro based exporting regions, and also redistributing the power supplied to load centers. Transmission expansion planning criteria must reflect the trade-off between investments in transmission, inducing more competition in generation, at the expense of increasing customer costs and a higher reliability level due to these investments. Measuring these trade-offs for hydrothermal systems requires taking into account multiple dispatch scenarios, and assessing network reliability for each scenario by a contingency analysis for each circuit outage. The network design problem that aims at choosing the best reinforcements among many candidate routes and voltage levels must therefore represent the transmission constraints for relevant dispatch scenarios and circuit contingencies. In this work a mixed integer disjunctive model is extended so as to deal with this problem minimizing the sum of investment costs and network reliability worth, measured by average interruption costs due to contingencies. Real world case system applications show that by means of a judicious choice of scenarios and contingencies, despite the increase of problem size the model is applicable, achieving a balanced choice between network reliability and investment requirements.

The Columbia River Treaty - an example of effective cross-border river regulation

With over 200 rivers around the world crossing international boundaries, internationally accepted treaties and agreements form the main framework for cross-border river development and operations. The Columbia River basin, in western North America, provides a significant example of effective cross-border river regulation. The river system is the fourth largest in North America but is called the "most powerful" river system on the continent, with an installed hydroelectric generating capacity of about 35,000 MW. The river originates in Canada and flows about 2,000 km to the Pacific Ocean in the United States. The river is operated under a treaty signed by the two countries in 1961, 13 years after a severe flood on the river that caused much damage in both countries. It was recognized that additional upstream storage regulation was needed to prevent similar flooding and that it would also help to improve power production at hydro plants in both countries. The Columbia River Treaty (CRT) is then an important planning and operations agreement to maximize benefits (multiple water uses) from the river for both countries. Under the CRT, Canada and US built storage regulation dams and agreed to operate the storage behind these dams in a coordinated manner to optimize for flood control and power needs. The objective of this work is to describe and analyze the CRT and to discuss the increasing public awareness of social and environmental issues in both countries, which has resulted in increasing pressures to modify river operations to optimize for other values in addition to power and flood control. While it is often difficult to find compatibility between the different goals of multiple water use, the CRT partners have maintained a cooperative attitude to find many "win-win" supplemental agreements, which have improved non-power operations on both sides of the border while maintaining the integrity of the CRT. Water resource conflict has long been discussed as one of the greatest threats to peace during the 21st century but early dialogue and earnest attempts to promote cooperation could, just as easily, turn such difficulties into a source of harmony rather than dispute. As will be seen, the CRT is a good example of such cooperation.

This work presents a methodology for energy transmission costs allocation, based on the Theory of Cooperative Games. The proposed method is based on the Aumann-Shapley scheme, which proposes a cost allocation in proportion to the average use of the transmission grid by each agent. The approach is shown to be robust, computationally efficient and presents many desirable characteristics in terms of economic coherence and isonomy. Computational results are presented for the Brazilian power system and compared with those obtained for three others methodologies: Long Run Marginal Cost (LRMC), the current method adopted in Brazil (a variant of the LRMC method) and Marginal Participation Factors.